# Enhancing Economic Sustainability with Credit Payment Services in a Dual-Channel Supply Chain

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Relevant Literature

## 3. Model Setting

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

## 4. Equilibrium Analysis

#### 4.1. Non-Credit Payment Services

**The scenario N.**Under the scenario of non-credit payment services, the supplier prohibits firms from providing credit payment services in the dual channel. The utility that the consumer obtains from the direct channel is ${u}_{1}=\rho v-{p}_{1}$ and the utility that the consumer obtains from the reselling channel is ${u}_{2}=v-{p}_{2}$, where ${p}_{1}$ (${p}_{2}$) is the retail price offered by the supplier (the retailer) in the direct (reselling) channel. Consumers purchase the product that provides them with the highest positive utility. As such, consumers who purchase from the direct channel meet $\rho v-{p}_{1}>0$ and $\rho v-{p}_{1}>v-{p}_{2}$, and the other consumers who purchase from the reselling channel meet $v-{p}_{2}>0$ and $v-{p}_{2}^{}>\rho v-{p}_{1}^{}$. We paid attention only on markets, where $\frac{{p}_{2}-{p}_{1}}{1-\rho}>\frac{{p}_{1}}{\rho}$ (i.e., $\rho >\frac{{p}_{1}}{{p}_{2}}$) to ensure the existence of both direct and reselling channels (Mantin et al. [29]). Based on this utility model, the demand functions for the direct channel and reselling channel are ${q}_{1}^{N}=\frac{{p}_{2}^{N}-{p}_{1}^{N}}{1-\rho}-\frac{{p}_{1}^{N}}{\rho}$ and ${q}_{2}^{N}=1-\frac{{p}_{2}^{N}-{p}_{1}^{N}}{1-\rho}$. Then, the profits of the supplier and retailer are:

#### 4.2. Credit Payment Services

**The scenario SN.**The consumer can obtain ${u}_{1}=\rho v-\tau {p}_{1}$ and ${u}_{2}=v-{p}_{2}$ from purchasing through the direct channel and the reselling channel respectively, where $\tau $ is price discount of credit payment services to consumers. Similarly, under the scenario SN, consumers who purchase from the direct channel meet $\rho v-\tau {p}_{1}>0$ and $\rho v-\tau {p}_{1}>v-{p}_{2}$, and the other consumers who purchase from the reselling channel meet $v-{p}_{2}>0$ and $v-{p}_{2}>\rho v-\tau {p}_{1}$. To ensure that both direct channel and reselling channel exist in the market and avoid trivial analyses, we restricted our attention to the following ranges $\frac{{p}_{2}^{SN}-\tau {p}_{1}^{SN}}{1-\rho}>\frac{\tau {p}_{1}^{SN}}{\rho}$(i.e., $\rho >\frac{\tau {p}_{1}^{SN}}{{p}_{2}^{SN}}$). Then, the demand functions in the direct and reselling channels are ${q}_{1}=\frac{{p}_{2}-\tau {p}_{1}}{1-\rho}-\frac{\tau {p}_{1}}{\rho}$ and ${q}_{2}=1-\frac{{p}_{2}-\tau {p}_{1}}{1-\rho}$, respectively. We obtained the payoffs of the firms under scenario SN as follows:

**The scenario SS.**Both the supplier and the retailer provide credit payment services. We assumed that the value discount of credit payment service is symmetric for the supplier and the retailer. The consumer utility in direct (reselling) channel is ${u}_{1}=\rho v-\tau {p}_{1}$ (${u}_{2}=v-\tau {p}_{2}$). Similarly, under the scenario SS, consumers who purchase from the direct channel meet $\rho v-\tau {p}_{1}>0$ and $\rho v-\tau {p}_{1}>v-\tau {p}_{2}$, and the other consumers who purchase from the reselling channel meet $v-\tau {p}_{2}>0$ and $v-\tau {p}_{2}>\rho v-\tau {p}_{1}$. Then, the demand functions are ${q}_{1}^{SS}=\frac{\tau {p}_{2}^{SS}-\tau {p}_{1}^{SS}}{1-\rho}-\frac{\tau {p}_{1}^{SS}}{\rho}$ and ${q}_{2}^{SS}=1-\frac{\tau {p}_{2}^{SS}-\tau {p}_{1}^{SS}}{1-\rho}$. Under the scenario SS, the expected payoffs are:

**The comparison of the scenario SN and the scenario SS.**Our study achieves the equilibrium outcomes under the scenarios of SN and SS. Then, we further investigated the retailer’s credit payment decision in the reselling channel when the supplier provides credit payment services in the direct channel.

**Lemma**

**1.**

- (i)
- when$0<\tau <1$and$\frac{\tau}{3-2\rho}<\delta <\tau $,${w}^{SN}>{w}^{SS}$and${p}_{1}^{SN}>{p}_{1}^{SS}$;
- (ii)
- when$0<\tau <1$and$\tau <\delta <min\left\{1,\frac{2\tau -\rho \tau}{\rho}\right\}$,${w}^{SN}<{w}^{SS}$and${p}_{1}^{SN}<{p}_{1}^{SS}$.

**Proposition**

**1.**

- (i)
- When$0<\tau <1$and$\frac{\tau}{3-2\rho}<\delta <\tau $, the retailer does not opt to carry out credit payment services in the reselling channel (i.e., scenario SN);
- (ii)
- When$0<\tau <1$and$\tau <\delta <min\left\{1,\frac{2\tau -\rho \tau}{\rho}\right\}$, the retailer prefers to provide credit payment services in the reselling channel (i.e., scenario SS).

## 5. Comparison and Discussion

#### 5.1. Credit Payment Decisions

**Proposition**

**2.**

- (i)
- When$0<\tau <1$and$\tau <\delta <min\left\{1,\frac{2\tau -\rho \tau}{\rho}\right\}$, the supplier provides credit payment services in the direct channel (i.e., the equilibrium outcome is scenario SS);
- (ii)
- When$0<\tau <1$and$\frac{\tau}{3-2\rho}<\delta <\tau $, the supplier does not provide credit payment services in the direct channel (i.e., the equilibrium outcome is scenario N).

#### 5.2. The Impact of Credit Payment

**Proposition**

**3:**

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Proof**

**of**

**Lemma**

**1.**

**Proof**

**of**

**Proposition**

**1.**

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**3.**

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**Figure 1.**Sequence of events and the cash flow diagram: (

**a**) sequence of events; (

**b**) the cash flow diagram under non-credit payment and under credit payment services.

**Figure 2.**The retailer’s optimal credit payment decision in the reselling channel (ρ = 0.5, τ = 0.4).

Paper | Discount of Opportunity Cost | Channel | Credit Payment Provider | ||
---|---|---|---|---|---|

Direct Channel | Reselling Channel | Agency Channel | |||

Zhen et al. [6] | ✓ | ✓ | ✓ | third-party platform, retailer, or bank | |

Tang et al. [5] | ✓ | ✓ | retailer | ||

Li et al. [27] | ✓ | manufacturer | |||

Yan et al. [17] | ✓ | ✓ | retailer | ||

Soman and Cheema [4] | ✓ | ✓ | retailer | ||

Chen et al. [13] | ✓ | supplier | |||

Huang [8] | ✓ | ✓ | retailer | ||

Our paper | ✓ | ✓ | ✓ | manufacturer, retailer |

Natation | Definition |
---|---|

ρ | Product value coefficient of the direct channel |

δ | Discount of cash opportunity cost |

τ | Price discount of credit payment services |

v | Value of the product to consumers |

w | Wholesale price |

p_{1} | Retail price of the direct channel |

p_{2} | Retail price of the reselling channel |

q_{1} | Demand potential of the direct channel |

q_{2} | Demand potential of the reselling channel |

π_{s} | Profit of the supplier |

π_{r} | Profit of the retailer |

π_{sc} | Profit of the supply chain |

Scenario | Explanation |
---|---|

N | Non-credit payment services of the direct and reselling channels when the supplier prohibits the supply chain from providing credit payment policy. |

SS | The retailer provides credit payment services in the reselling channel when the supplier allows to provide credit payment in the direct channel. |

SN | Non-credit payment services of the reselling channel when the supplier provides credit payment in the direct channel. |

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## Share and Cite

**MDPI and ACS Style**

Huang, X.; Xu, L.; Liu, J.; Huang, Y.
Enhancing Economic Sustainability with Credit Payment Services in a Dual-Channel Supply Chain. *Sustainability* **2022**, *14*, 8295.
https://doi.org/10.3390/su14148295

**AMA Style**

Huang X, Xu L, Liu J, Huang Y.
Enhancing Economic Sustainability with Credit Payment Services in a Dual-Channel Supply Chain. *Sustainability*. 2022; 14(14):8295.
https://doi.org/10.3390/su14148295

**Chicago/Turabian Style**

Huang, Xinqian, Liang Xu, Jun Liu, and Ying Huang.
2022. "Enhancing Economic Sustainability with Credit Payment Services in a Dual-Channel Supply Chain" *Sustainability* 14, no. 14: 8295.
https://doi.org/10.3390/su14148295